Since I did not get a level 5 felony during any missions I took it upon myself to cause some chaos on Alcatraz Island. I stealthily cleared out the area in the north where the Bratva gang hangs out. In a building here, there is a place you will want to hole-up once you have the heat on you. It is the top floor of the boat house where there is a part of the floor you can hack to open. This floor hatch leads to a pretty secure area that you can hide out in to escape your wanted level. Also, there are three doors and a stair case leading into the area before you drop into the floor, but you can cover those easily and you can place some explosive traps throughout the floor.
Once you have removed the Bratva gang from Alcatraz, Stay near the area (so they do not respawn) and beat up some of the tourists on the island (it should take about 5-7 people and you should be at a level 3 felony). Once the cops show up shoot a couple and retreat to the hole-up spot I previously mentioned. Continue to shoot the cops that appear, you may need to open a door or two to keep the felony going. Once you get to level 5, hack the floor to open it and hack it again to close it as you jump down into a pretty secure room. Hide out down here until "the heat is off you." There is one door in this room, but I never had the cops come search this area. If you happen to get one that opens the door, stealth-melee kill them and after you escape the achievement should pop.
Edit: Noted from the Comments below by Melomonster721 and confirmed by Cclan2, it appears you need to be in a single-player session for the achievement to pop. It would likely be the best practice to disable all online play while attempting to get the achievement.